8H38 Sunday December 30, 2001. I am ready to start signal compression on the beam-formed, band-width-limited 2-hour signal files (e.g.: r0124506.27w -> r0124506.27d using rafdet.pro).
But first, I need to make some cross checks to understand the data. (And maybe some day I should actually do a detailed numerical verification - later.) I will investigate signal sizes for this data, the first run with a RAFOS signal.
Here is a 2-hour beam-formed signal. The rms can be estimated from Horowitz's rule of thumb, that the rms is about equal to 1/8 of the peak-to-peak "envelope." I estimate this to give rms = 1/8 * 3000 = 400. An exact calculation gives 382.593 for the full 7,376,896 - point time series.
Here is the same data, mixed with 260 Hz and downsampled by averaging 128 points together. From the graph, the rms should come out to be 120 * 1/8 = 15. Exact calculation gives 17.56 for the full 57,632 - point time series.
I have realized that mixing with a sine wave of amplitude 1 results in reducing the size of a signal by a factor of 1/2, as well as shifting the frequency. So, taking this into account, we can predict the rms of the .w file from that of the .b file. I will assume that the power spectrum is flat, and that the bandwidth of both signals is proportional to the sampling rate. Then
rmsw-pred = rmsb-obs * (BWw/BWb)1/2 *(1/2) =382.6 * (1/128)1/2 * (1/2) = 16.9The agreement is so good as to be fortuituous (no reason for the power spectrum to be flat).
16H01. Note the features in the narrow-band data, in order of maximum amplitude on the graph above:
|Large signals after narrow-band filtering, r0124506.27|
18:48 Monday December 31, 2001. Still a little time left before New Year's Eve starts.
I have just realized that the file I am working on starts at 6:27 Zulu and so is not expected to have any RAFOS signals. I was chagrined at not being able to see them. Now I feel a little better. I will try to hone up my detection scheme on this null file, then try it on some others.
I am pretty sure that the raw (but beam-formed) signal (r0124506.27b) will not show the RAFOS signals. Their power level is below the integrated power from zero to 400 Hz. However, I think that the band-pass signal should show it. I am a little unclear on its bandwidth, and even less clear on the degree of aliasing admitted by the procedure of combining points. However, as a first guess I would say that the bandwidth is twice the Nyquist frequency, or about 8 Hz - I am not clear about negative frequencies. At any rate, I think that the RAFOS signal should be visible in this frequency band.
A way to make the signal stand out more would be to square and average over 80 seconds. This should be pretty easy. I will try it . . . here is the result. The general level of the averaged squared signal, around 350, corresponds quite well to the square of the rms given in the table above. (Just a consistency check.)
This might be the end of my research for the year 2001.